This application claims benefit of Japanese Application Nos. 2001-56473 and 2001-332290 filed in Japan on 3.1.2001 and 10.30,2001, the contents of which are herein incorporated by this reference.
The present invention relates generally to an optical system, and more particularly to an optical system used with an image pickup optical system having zooming (scaling) and focusing functions, etc.
Zoom image pickup optical systems constructed of free-form surface prisms, for instance, are disclosed in JP-A""s 08-292372, 11-317894 and 11-317895.
However, the optical system of JP-A 08-292372 is designed for zooming or scaling by movement of a plurality of prisms. This requires an increase in size to provide sufficient space for the movement of the prisms in the system. Moreover, high accuracy needed for a mechanism for precise linear movement of the prisms makes the system structurally complicated providing obstacles to assembling the system and increased cost.
Similarly, the zooming or scaling mechanism of JP-A 11-317894, and JP-A 11-317895 has the same structural problem because of the movement of transmitting lens optical element.
With the prior art, it is thus impossible to achieve any zoom (scaling) optical system of smaller size because of the required space for movement of the optical element. This optical element itself has aberration problems, and renders optical parameters so likely to vary by large amounts that it may not be used.
Ordinary control of zooming (scaling) or focusing is generally carried out by moving several optical elements in an optical system along the optical axis. However, problems with this control mode are that it is difficult to move the optical elements completely parallel to the optical axis, causing tilting and decentration of the optical elements and, hence, degradation of images. Especially when a zooming (scaling) optical system is designed for an image pickup system of smaller size, very stringent, if not impossible, accuracy is imposed on the movement.
In view of such problems of the prior art, one object of the present invention is to provide an optical system of so simplified construction that its focal length, image-formation position, etc. can be controlled by bending the optical system to shift a light beam passing through the optical system and thereby making selective use of an arbitrary portion of the optical system.
According to one aspect of the invention, this object is achieved by the provision of an optical system, characterized in that said optical system is transformed to bend an optical axis thereof, so that paraxial amounts thereof can be varied.
According to another aspect of the invention, there is provided an image-formation optical system comprising at least two optical elements, characterized in that said at least two optical elements are mutually decentered, thereby varying the properties of said optical system.
Preferably in this embodiment, the optical system should be constructed of a first optical element located on the object side thereof for forming a primary image and a second optical element for projecting the primary image onto an image plane of the optical system. This second optical element is decentered by rotation with the center of rotation defined by the vicinity of the primary image.
Preferably in this embodiment, at least one of the first and second optical elements should be formed of an optical element having at least one rotationally asymmetric surface.
In this case, said at least one rotationally asymmetric surface may be defined by a continuous surface.
If the second optical element is decentered by rotation with respect to the first optical element, it is then possible to vary at least one of the focal length, image-formation position (focus), image-formation magnification and principal point of the optical system.
According to a specific preferred embodiment of the invention, there is provided an optical system comprising at least two optical elements, each having a rotationally asymmetric free-form surface, or a first optical element located on the object side of the optical system for forming a primary image and a second element for projecting the primary image, wherein the second optical element is decentered with the center of rotation defined by the vicinity of the primary image so that a light beam incident on the second optical element is reflected and bent at an arbitrarily selected central portion of the second optical element for zooming (scaling) at the second optical element, and the second optical element has an angle xcex8 of rotation run-out that satisfies the following condition:
0xc2x0 less than xcex8 less than 90xc2x0xe2x80x83xe2x80x83(1)
Preferably in this embodiment, the optical system should satisfy the following condition:
0.5 less than |Fy/Fx| less than 2xe2x80x83xe2x80x83(2)
Here Fx is the focal length of the optical system in an X direction and Fy is the focal length of the optical system in a Y direction provided that the direction of decentration of the optical system defines a Y-axis direction, a plane parallel with an axial chief ray defines a Y-Z plane and a direction perpendicular to the Y-Z plane defines the X-direction.
Why the aforesaid arrangements are used in the invention, and what is achieved thereby is now explained.
FIG. 1 is a schematic view illustrative of how light rays behave in a meridional section of an optical element S at which some large coma occurs with substantially well corrected spherical aberration, curvature of field, astigmatism, longitudinal chromatic aberration and chromatic aberration of magnification. With some considerable coma occurring, rays {circle around (1)}, {circle around (2)} and {circle around (3)} emanating at different angles of view from an object O are incident on an image plane I at different positions. Accordingly, as aperture positions P1, P2 and P3 of this optical element S displace substantially vertically with respect to an optical axis (note that an optical axis is defined by an axial principal ray passing through the center of an entrance pupil and arriving at the center of the image plane; however, the optical axis used herein is defined by an axial principal ray passing through the center of each aperture P1, P2, P3 and arriving at the center of the image plane), the rays {circle around (1)}, {circle around (2)} and {circle around (3)} passing through the optical element S vary in position and angle, so that they are incident on the image plane I at different heights H1, H2 and H3. Consequently, the image-formation magnification of the object O on the image plane I varies. In other words, zooming (scaling) can be effected by shifting each aperture substantially vertically to the optical axis. On the same principles, the image-formation position and principal point, too, can be controlled by shifting the pupil position substantially vertically to the optical axis. It is here noted that since the aperture positions are displaceable vertically to the direction coming out of the paper, for instance, zooming (scaling) may be carried out by displacement within the plane of the paper and focusing may be effected by displacement in the direction coming out of the paper.
As an optical system having at least two optical elements S1 and S2 as typically shown in FIG. 2(a) is decentered as shown in FIG. 2(b), an aperture A located on the object side of the first optical element S1 is projected by the first optical element S1 as an aperture image Axe2x80x2 in the vicinity of the second optical element. Then, as the first and second optical elements S1 and S2 are relatively transformed (decentered), the projected image Axe2x80x2 for the aperture A projected by the first optical element S1 is shifted with respect to the second optical element S2. On the other hand, it is possible to construct the second optical element S2 with at least one rotationally asymmetric optical surface; it is possible to construct an optical element whose power varies on an arbitrary portion of that optical surface. By using at least one such optical element and shifting at least two optical elements relatively thereby bending the optical axis, it is possible to vary at least one paraxial amount out of the focal length, image-formation position, image-formation magnification, principal point position, etc.
More preferably, the rotationally asymmetric optical surface should be in a continuous form, because the aforesaid optical amount can be varied continuously. Of course, if the rotationally asymmetric optical surface is in a discontinuous form, then the aforesaid optical amount can be varied discontinuously.
In FIG. 2, the first optical element S1 is used as the optical element for forming a primary image Ixe2x80x2 and the second optical element S2 is designed as a variable projection magnification optical element. Even more preferably, however, the first optical element S1 is designed as a variable focal length optical element so that the size of the primary image Ixe2x80x2 is variable, thereby projecting this primary image Ixe2x80x2 by the second optical element S2 onto the image plane I at the same magnification. Moreover, both the groups can be separately varied.
In FIG. 2, the first optical element S1 is fixed and the second optical element S2 is decentered. However, it is noted that the reverse also holds true. In the present invention, the relative decentration of both the elements is thus of importance.
Even more preferably, the second optical element S2 should be rotated around the vicinity of the primary image Ixe2x80x2, because the image plane I can be rotated together with the second optical element S2, so that the arrangement of the optical system can be much more simplified.
It is also acceptable that the second optical element is kept from rotation around the primary image Ixe2x80x2. In other words, when the image position is displaced, it is possible to make correction for the center of the image by shifting an image pickup device, photographic film or the like in alignment with the displaced image position.
In FIG. 2, the primary image Ixe2x80x2 is located between the first optical element S1 and the second optical element S2; however, it may be located at an arbitrary position rather than between the first optical element S1 and the second optical element S2. In this case, too, it is of importance to locate the second optical element at that position by rotation around the primary image Ixe2x80x2 formed by the first optical element S1.
When the primary image Ixe2x80x2 is located at infinity, it is preferable to translate the second optical element S2.
More preferably, decentration should be carried out three-dimensionally, so that zooming (scaling) can be by decentration in one plane and focusing by decentration in a plane perpendicular thereto.
While, for the sake of convenience, the first and second optical elements S1 and S2 have been described as being separate from each other, it is understood that the first and second optical elements S1 and S2, if they have the same action, may be formed of a transparent elastomer material as one piece.
The arrangement (optical element or system) designed to enable at least one of focal length, image-formation position, image-formation magnification and principal point position to be controlled by the relative transformation (decentration) of the first and second optical elements S1 and S2, as described above, may be applied to those such as refractive optical systems, reflective optical systems and reflective/refractive optical systems, each having at least one continuous, rotationally asymmetric surface.
Typically, a free-form surface, as defined by the following defining equation (a), is used as the rotationally asymmetric surface. In this defining equation, the Z axis defines the axis of the free-form surface.                     Z        =                                            cr              2                        /                          [                              1                +                                                                            xe2x80x83                                                        ⁢                                      {                                          1                      -                                                                        (                                                      1                            +                            k                                                    )                                                ⁢                                                  xe2x80x83                                                ⁢                                                  c                          2                                                ⁢                                                  xe2x80x83                                                ⁢                                                  r                          2                                                                                      }                                                              ]                                +                                    ∑                              j                =                2                            66                        ⁢                          xe2x80x83                        ⁢                                          C                j                            ⁢                              xe2x80x83                            ⁢                              X                m                            ⁢                              xe2x80x83                            ⁢                              Y                n                                                                        (        a        )            
Here the first term of equation (a) is a spherical term and the second term is a free-form surface term.
In the spherical term:
c: the curvature of the apex,
k: the conic constant, and
r={square root over ( )}(X2+Y2)
The free-form surface term is:             ∑              j        =        2            66        ⁢          xe2x80x83        ⁢                  C        j            ⁢              xe2x80x83            ⁢              X        m            ⁢              xe2x80x83            ⁢              Y        n              =                    C        2            ⁢      X        +                  C        3            ⁢      Y        +                  C        4            ⁢              X        2              +                  C        5            ⁢      XY        +                  C        6            ⁢              Y        2              +                  C        7            ⁢              X        3              +                  C        8            ⁢              X        2            ⁢      Y        +                  C        9            ⁢              XY        2              +                  C        10            ⁢              Y        3              +                  C        11            ⁢              xe2x80x83            ⁢              X        4              +                  C        12            ⁢              xe2x80x83            ⁢              X        3            ⁢              xe2x80x83            ⁢      Y        +                  C        13            ⁢              xe2x80x83            ⁢              X        2            ⁢              xe2x80x83            ⁢              Y        2              +                  C        14            ⁢              xe2x80x83            ⁢              XY        3              +                  C        15            ⁢              xe2x80x83            ⁢              Y        4              +                  C        16            ⁢              xe2x80x83            ⁢              X        5              +                  C        17            ⁢              xe2x80x83            ⁢              X        4            ⁢              xe2x80x83            ⁢      Y        +                  C        18            ⁢              xe2x80x83            ⁢              X        3            ⁢              xe2x80x83            ⁢              Y        2              +                  C        19            ⁢              xe2x80x83            ⁢              X        2            ⁢              xe2x80x83            ⁢              Y        3              +                  C        20            ⁢              xe2x80x83            ⁢              XY        4              +                  C        21            ⁢              xe2x80x83            ⁢              Y        5              +                  C        22            ⁢              xe2x80x83            ⁢              X        6              +                  C        23            ⁢              xe2x80x83            ⁢              X        5            ⁢              xe2x80x83            ⁢      Y        +                  C        24            ⁢              xe2x80x83            ⁢              X        4            ⁢              xe2x80x83            ⁢              Y        2              +                  C        25            ⁢              xe2x80x83            ⁢              X        3            ⁢              xe2x80x83            ⁢              Y        3              +                  C        26            ⁢              xe2x80x83            ⁢              X        2            ⁢              xe2x80x83            ⁢              Y        4              +                  C        27            ⁢              xe2x80x83            ⁢              XY        5              +                  C        28            ⁢              xe2x80x83            ⁢              Y        6              +                  C        29            ⁢              xe2x80x83            ⁢              X        7              +                  C        30            ⁢              xe2x80x83            ⁢              X        6            ⁢              xe2x80x83            ⁢      Y        +                  C        31            ⁢              xe2x80x83            ⁢              X        5            ⁢              xe2x80x83            ⁢              Y        2              +                  C        32            ⁢              xe2x80x83            ⁢              X        4            ⁢              xe2x80x83            ⁢              Y        3              +                  C        33            ⁢              xe2x80x83            ⁢              X        3            ⁢              xe2x80x83            ⁢              Y        4              +                  C        34            ⁢              xe2x80x83            ⁢              X        2            ⁢              xe2x80x83            ⁢              Y        5              +                  C        35            ⁢              xe2x80x83            ⁢              XY        6              +                  C        36            ⁢              xe2x80x83            ⁢              Y        7            
Here Cj is an integer of 2 or greater) is a coefficient.
In general, the aforesaid free-form surface has no symmetric surface at both the X-Z plane and the Y-Z plane. However, by reducing all the odd-numbered terms for X to zero, that free-form surface can have only one symmetric surface parallel with the Y-Z plane. By reducing all the odd-numbered terms for Y to zero, the free-form surface can have only one symmetric surface parallel with the X-Z plane.
Among the defining formulas for other free-form surface, there is Zernike polynomial given by the following formula (b). The shape of this surface is given by the following formula. The axis for Zernike polynomial is given by the Z axis for the defining formula. The rotationally asymmetric surface is defined by polar coordinates for the height of the Z axis with respect to the X-Y plane provided that R is the distance from the Z axis within the X-Y plane and A is the azimuth angle around the Z axis, as expressed by the angle of rotation measured from the X-axis.
x=Rxc3x97cos(A) 
i y=Rxc3x97sin(A) 
i Z=D2 
+D3R cos(A)+D4R sin(A) 
+D5R2 cos(2A)+D6(R2xe2x88x921)+D7R2 sin(2A) 
+D8R3 cos(3A)+D9(3R3xe2x88x922R)cos(A) 
xe2x80x83+D10(3R3xe2x88x922R)sin(A)+D11R3 sin(3A)+D12R4 cos(4A)+D13(4R4xe2x88x923R2) cos(2A)
+D14(6R4xe2x88x926R2+1)+D15(4R4xe2x88x923R2)sin(2A) 
+D16R4 sin(4A)+D17R5 cos(5A)+D18(5R5xe2x88x924R3)cos(3A) 
+D19(10R5xe2x88x9212R3+3R)cos(A)
+D20(10R5xe2x88x9212R3+3R)sin(A) 
+D21(5R5xe2x88x924R3)sin(3A)+D22R5 sin(5A)+D23R5 cos(6A)+D24(6R6xe2x88x925R4)cos(4A)
+D25(15R6xe2x88x9220R4+6R2)cos(2A) 
+D26(20Rxe2x88x9230R4+12R2xe2x88x921) 
+D27(15R6xe2x88x9220R4+6R2)sin(2A) 
+D28(6R6xe2x88x925R4)sin(4A)+D29R6 sin(6A)xe2x80x83xe2x80x83(b)
Here Dm is a coefficient provided that m is an integer of 2 or more. It is noted that when this free-form surface is designed in the form of an optical system symmetric with respect to the X-axis direction, D4, D5, D6, D10, D11, D12, D13, D14, D20, D21, D22, . . . are used.
While the aforesaid defining formula is given to exemplify the surface of a rotationally asymmetric, curved surface, it is understood that even with any other defining formula the same effect would be obtainable.
Among other defining formulae for the free-form surface, there is the following one (c):
Z=xcexa3xcexa3CnmXY
When expanded with respect to k=7 (the seventh term) as an example, this may be expressed by the following formula:
Z=C2 
xe2x80x83+C3Y+C4|X|
+C5Y2+C6Y|X|+C7X2 
+C8Y3+C9Y2|X|+C10YX2+C11|X3|
+C12Y4+C13Y3|X|+C14Y2X2+C15Y|X3|+C16X4 
+C17Y5+C18Y4|X|+C19Y3X2+Y20Y2|X3|C21YX4+C22|X5|
+C23Y6+C24Y5|X|+C25Y4X2+C26Y3|X3|+C27Y2X4+C28Y|X5|+C29X6 
+C30Y7+C31Y6|X|+C32Y5X2+C33Y4|X3|
+C34Y3X4+C35Y2|X5|+C36YX6+C37|X7|xe2x80x83xe2x80x83(c)
It is noted that anamorphic or toric surfaces may be used as rotationally asymmetric surfaces.
In the optical element and optical system of the invention, powers Px and Py are defined by incidence of a parallel light ray spaced slightly away from the axial principal ray with respect to light rays in two directions in any orthogonal Y-Z and X-Z planes including the optical axis, as taught in JP-A 11-194267, paragraph
The Fy/Fx ratio is determined from the focal lengths Fx and Fy that are the reciprocals of the powers.
As exemplified in Examples 1 to 5 given later, the optical system of the invention is made up of two optical elements, each formed of a rotationally asymmetric free-form surface. A first optical element is located on the object side of the optical system to form a primary image and a second optical element is provided to project the primary image. The second optical element is decentered with the center of rotation defined by the vicinity of the primary image, so that a light beam incident on the second optical element is reflected and bent at a portion arbitrarily selected out of the second optical element for zooming (scaling) at the second optical element. Preferably in this case, the angle xcex8 of rotation run-out of the second optical element should satisfy the following condition (1):
0xc2x0 less than xcex8 less than 90xc2x0xe2x80x83xe2x80x83(1)
When the lower limit of 0xc2x0 to this condition is not reached, the selection of the optical path per se is impossible to make and, hence, it is impossible to vary the optical parameters. Exceeding the upper limit of 90xc2x0 is not preferable because the size of the second optical element becomes large.
It is then of great importance to satisfy the following condition (1xe2x80x941):
10xc2x0 less than xcex8 less than 45xc2x0xe2x80x83xe2x80x83(1xe2x80x941)
When the lower limit of 10xc2x0 not reached, partial power changes in the continuous, rotationally asymmetric surface used in the second optical element become noticeable, leading to a failure in achieving satisfactory aberration states all over the screen. Exceeding the upper limit of 45xc2x0 is not preferable because of an increase in the size of the second optical element.
Here let the direction of decentration of the optical system represent the Y-axis direction, a plane parallel with an axial principal ray denote the Y-Z plane, a direction perpendicular to the Y-Z plane stand for an X direction, and Fx and Fy indicate the focal lengths of the optical system in the X and Y directions. Then, it is important to satisfy the following condition (2):
0.5 less than |Fy/Fx| less than 2xe2x80x83xe2x80x83(2)
Upon the lower limit of 0.5 to this condition not being reached, the focal length becomes too long in the X direction relative to the Y direction, so that an image in the X direction becomes too large upon image-formation, resulting in a transversely oblong image. When the upper limit of 2 is exceeded, on the other hand, the focal length becomes too short in the X direction relative to the Y direction, so that an image in the X direction becomes too small, resulting in a longitudinally oblong image.
For an optical system whose focal length is variable as contemplated herein, it is of vital importance to satisfy the aforesaid condition (2) even where the focal length is varying. Unless the aforesaid condition (2) is satisfied in all states where the optical system is placed at the wide-angel to telephoto end or focused on a point at infinity to a nearby point, image distortion changes become unnatural during zooming (scaling) or focusing, resulting in a very difficult-to-observe image.
More preferably, it is of importance to meet the following condition (2-1):
0.7 less than |Fy/Fx| less than 1.3xe2x80x83xe2x80x83(2-1)
The same as in condition (2) is true for the upper and lower limits.
Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification.
The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims.